There is a contractual requirement to demonstrate with 90% confidence that a veh

Question

There is a contractual requirement to demonstrate with 90% confidence that a vehicle can achieve a 100 km mission with a reliability of 99%. The acceptance test is performed by running 10 vehicles over a 50,000- km test track.

Contractual MTTF=9950km

What is the maximum number of failures that can be experienced on the demonstration test without violating the contractual requirement? (Note: Assume an exponential distribution.

-In other words, How can I demostrate this contractual MTTF given the other information in the question (i.e. how many ofthe 10 cars can fail on the 50,000km test track using a 90% confidence in order to demontrate MTTF-9950km?

Explanation / Answer

Reliability R = 99%,

Confidence 90% so failure rate = 1-0.90

Or = 0.1

x = 50,000 km

(a)        Now as R = 1- (1- e-2(*t))

            0.90 = 1 – (1 – e-2(0.1*t))

            1 – e-2(0.1t) = 0.1

            e-2(0.1t) = 0.9

Taking log both sides-

-2(0.1t) = ln(0.9)

-2(0.1t) = -0.105

t = 5.26 km

The system MTTF can be calculated by-

M/(Number of vehicles*)    = 1/(2*0.1)

M/(6*0.1) = 1/0.2

M = 3 Km

M = 3 km

(b)       The maximum number of failures that can be experienced are-

            N = Total distance/mean time/distance between failure

            N =50,000/5.26

            N = 9505.70

            N = 9506 failures.

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